You are here
Question 3 - Composite functions and one-one onto - Chapter 1 Class 12 Relation and Functions
Last updated at July 24, 2026 by Teachoo
Composite functions and one-one onto
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
- To prove one-one & onto (injective, surjective, bijective)
- Composite functions
-
Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 5 questions, selected from your answers, mistakes, and progress.
Transcript
Question 3 Show that if f : A → B and g : B → C are onto, then gof : A → C is also onto. Since g : B → C is onto Suppose z ∈ C, then there exists a pre-image in B Let the pre-image be y Hence, y ∈ B such that g (y) = z Similarly, since f : A → B is onto If y ∈ B, then there exists a pre-image in A Let the pre-image be x Hence, x ∈ A such that f(x) = y Now, gof : A → C gof = g(f(x)) = g (y) = z So, for every x in A, there is an image z in C Thus, gof is onto.
